SVG Model falling through the ground?
There are several problems in your file:


All the objects have un-applied scale, which can cause rigid-body simulations to behave strangely. Apply the scale to the objects mesh data with CtrlA>Scale.
The SVG/star object's origin is not centered. The origin is used to determine the center of mass, so if it's in an odd place (as in this case), it will cause strange behavior. Center the origin with CtrlShiftAltC> Origin to Center of Mass.
The SVG mesh has some strange topology/overlapping faces:

The SVG mesh is a little messy, with non-manifold geometry and overlapping faces:



Try deleting all the faces and then adding loop cuts at the intersections to get a mesh like this (click for slower speed):






Optimizations:

There are few minor optimizations you can make too:


Make the floor solid. Rigid-body simulation likes manifold meshes more than non-manifold meshes (such as a plane). 

Another advantage to using a floor with thickness is you can use the Box collision shape for it, which tends to be faster and more stable than the Mesh option.
Use the Box option for the cube. It's always better to use the primitive collision shapes where possible.
Use the mesh collision shape on the SVG. Because the SVG has concave parts, only mesh will allow it to collide accurately.


Result



Example .blend